Attribute reduction for sequential three-way decisions under dynamic granulation

In real-world decision making, sequential three-way decisions are an effective way of human problem solving under multiple levels of granularity. Making the right decision at the most optimal level is a crucial issue. To this end, we address the attribute reduction problem for sequential three-way decisions under dynamic granulation. By reviewing the existing definitions of attribute reducts, a new attribute reduct for sequential three-way decisions is defined, and a corresponding monotonic attribute significance measure is designed. An attribute reduction algorithm satisfying the monotonicity of the probabilistic positive region is developed. The relationships of the different attribute reducts, the probabilistic positive regions and the probabilistic positive rules for decision-theoretic rough set models are further discussed under global view, local view and sequential three-way decisions. Experimental results demonstrate that our method is effective. This study will provide a new insight into the attribute reduction problem of sequential three-way decisions.